The stylish, four-minute rendition of the 1973 track features high-ranking artists, ranging from the country singer Tammy Wynette to the soprano Lesley Garrett, who each sing one line of Reed's song. And it had an extraordinary response from viewers.
The advert was designed to demonstrate the wide variety of musical styles brought to a BBC audience and funded by the licence fee. During the first two weeks of transmission it prompted hundreds of calls, requests for repeated screenings, and demands for its release as a CD.
"We have never had anything like this before," said a BBC spokeswoman. "Other recent promotional films, for example the funny ones with Michael Palin and with Reeves and Mortimer, as well as the one with the cast of Eastenders, have gone down extremely well when we have done market research, but we have never actually had people ringing in to praise them."
The record can only hit the shops if the corporation's legal team completes complex negotiations with the separate representatives of the 30 acts who participated. Those in charge of the project hope to announce the release of a CD in aid of Children in Need at some point this week.
Among superstars featured in the line-up are Elton John, Bono, Suzanne Vega, Boyzone, M People and Tom Jones. Lou Reed himself also appears, as does David Bowie who produced, with the late Mick Ronson, the LP Transformer from which the song is taken. Until now the album's most famous song was Walk on the Wild Side.
The video was the brainchild of Jane Frost, a huge fan of the Reed song and the corporation's Head of Corporate and Brand Marketing. Perhaps she also saw a certain appropriateness in the song's refrain "You're going to reap just what you sow", when it came to evangelising about the licence fee.
Work on the project has been going on for most of the year and it was first screened on television last month. This Friday it will make the first of several appearances at selected cinemas.
Lou Reed allowed the BBC to use his song for free while all the other artists, including Dr John, Courtney Pine, Joan Armatrading and the baritone Thomas Allen, received a nominal fee of pounds 250.
The BBC has strenuously denied reports that the video cost pounds 2m to make. "It was nothing like that much. We did it very cheaply because of the goodwill of the artists and we stayed within our promotional budget," said the spokeswoman.
The advertising agency Leagas Delaney teamed up with the BBC's own production staff and with music producers Mark Sayer and Tolga Kashif and director Gregory Rood to produce the film.
In order to bring out the CD the BBC must now secure permission from all the singers involved to use their performances without making any further payment. "The letters have already gone out and we have already had some positive responses," the spokeswoman said.